Straighten the series of vertices in UV editor
If you don't want to straighten your UV islands (How do I straighten UV maps?), cause in your case it might be very time consuming you might repeat the steps I've shown in the .gif below.
In Edit Mode select all faces (A), press U-->Lightmap Pack-->OK. Now select one of the face to make it active, then again press U-->Follow Active Quads-->OK. Your UV island is straight now. Adjust it using G, R and S to fit the image. If your mapped image is upside down just scale it negative 1 (S,Y,-1).